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One-fourth of Massachusetts middle-schoolers and 16 percent of high school students report enduring bullying at school, according to a federal report released yesterday that puts the state at the center of the national discussion over the issue.

For the first time, Massachusetts health authorities included questions about bullying in a survey regularly given to gauge the health and behaviors of the state’s students, and the findings not only define the scope of the problem, but also suggest the cause. Most notable was the link between violence at home and bullying at school.

The report found that students who said they had been involved in bullying, as both a perpetrator and a victim, were five times more likely to report they had been hurt physically by a family member, compared to those who said they were neither a victim nor a bully. And they were substantially more likely to have witnessed violence against other family members.

The study was released a year after Governor Deval Patrick signed a law requiring schools to adopt clear procedures for reporting and investigating cases of bullying, as well as methods for preventing retaliation against those who report problems.

Because Massachusetts is the first state to conduct a bullying survey in this manner, it is not possible to compare the results with other states to determine whether bullying is more or less common in Massachusetts, state officials said.

As schools and health de partments grapple with bullying and its myriad consequences, researchers said the findings from the US Centers for Disease Control and Prevention and the state Department of Public Health underscore the need for educators to recognize the strong link to family dynamics in students’ lives.

“These children are learning [violent behavior] in their families and behaving the same way in their social relationships with their peers,’’ said Elizabeth Englander, a psychology professor at Bridgewater State University and director of the Massachusetts Aggression Reduction Center, which conducts research and runs antibullying programs in many public schools.

“I think we all know there are many more cases of [family] abuse than we can detect,’’ she said.

The survey, conducted in 2009 and released yesterday, also found that students who said they were both victims and perpetrators were significantly more likely than other students to report they had attempted suicide or seriously considered it in the previous 12 months.

And they were much more likely to say they drank or used drugs, the report found.

“Sometimes, people who we have thought of as perpetrators are actually very vulnerable themselves,’’ said John Auerbach, Massachusetts public health commissioner.

Auerbach’s department conducted the student survey and is helping the state’s Education Department implement the antibullying law. He said the findings will help his agency train counselors and educators to better pinpoint potential problems.

“If we are working with women who are victims of domestic violence, for instance, it is clear the children would need special supports to lessen the likelihood that they are victims or bullies’’ or both victims and perpetrators, Auerbach said.

“This also suggests that when we are working with adolescents with substance abuse problems, we should be screening them to see if part of what’s going on in their lives is related to violence,’’ he said.

Every two years, Auerbach’s department surveys thousands of Massachusetts public school students about a variety of behaviors. The latest findings are based on the department’s 2009 survey, which for the first time included questions about bullying.

The anonymous survey of roughly 6,000 students, conducted with pen and paper, was completed during one class period in 138 public middle and high schools. The findings took into account differences among age, sex, race, ethnicity, and nonresponses.

Researchers from the CDC helped analyze the data.

Steve Marcelin, a senior at the Social Justice Academy high school in Hyde Park, said the numbers ring true. The 18-year-old, who moved to Massachusetts from Haiti five years ago, said he was bullied and taunted during eighth and ninth grades as he struggled to learn English.

“Most of the time I felt powerless,’’ Marcelin said. “I would try to, in school, keep a straight face, but at home I would cry.’’

Marcelin said he did not contemplate suicide, nor did he strike out and bully someone else. He credits support from his family for helping him through those dark days.

“My parents are mostly at work, so they don’t have that much time to go to the school,’’ he said. “But they would tell me things to try and lift up my spirit.’’

The state survey found that 13 to 15 percent of victims who said they had been bullied reported that they either had witnessed violence in their families in the past year or had been physically hurt by a family member.

The percentages were even higher among bullies and those who said they were both bully and victim. At the high school level, 31 percent of students who said they were both a perpetrator and a victim reported having witnessed family violence in the past year.

A separate study by the Massachusetts Aggression Reduction Center further underscores the scope of the problem. Preliminary results from a survey of 21,000 third- through 12th-graders suggest roughly half of students who identified themselves as bullies also said they had been victims of bullying.

Glenn Koocher, executive director of the Massachusetts Association of School Committees, said the findings from yesterday’s federal report do not surprise him. They starkly illustrate the increasing challenges schools face, he said.

Family violence is “beyond our control, but not beyond our responsibility, because society has put that on us to deal with it,’’ Koocher said.

Bullying, he said, “drains the emotions of principals and teachers . . . and all of this gets in the way of learning.’’